Convergence of the solution of the one-phase Stefan problem when the heat transfer coefficient goes to zero

We consider the one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face, with a heat transfer coefficient (proportional to the Biot number) h>0. We study the limit of the temperature θh and the free boundary sh when h goes to zero, and we also obtain an order of convergence. The goal of this paper is to do the mathematical analysis of the physical behavior given in [C. Naaktgeboren, The zero-phase Stefan problem, Int. J. Heat Mass Transfer 50 (2007) 4614–4622].